Rendering a scene with shaderless objects results in a completely black image
It's not going to work because of child particles

Unfortunately, since you are rendering child particles, you can't achieve your goal at the moment (Blender 2.79).

This is because the Particle Info node 


  ... currently only supports parent particles. Info from child particles is not available.


I don't know the roadmap for this.

Other details

First, you are currently seeing a good "material" view, because it doesn't rely on Cycles. But if you change to the "rendered" view (you don't have to make an actual render, but it's practically the same), it falls back to black.



Now, even if you disable the "children" in your particle system, it's not going to get any better



this is because your material is, indeed, "shaderless"! 

If you add a shader (like the "Emission Shader"), though:



Voilà! 

Unfortunately, though, it won't work if you enable child particles again.